Do radio receivers use any power from a transmitter?

• Turning on your TV or radio does not cost the broadcaster more money, because broadcast transmissions would otherwise be dissipated by some other object.
• some energy is drawn in by the receiver circuit of the radio.

Both statements are true. Do you think one contradicts the other? I think of it as analogous to the big decorative water sprinkler at the local park. (I agree that "dissipated in the air" seems unlikely).

• Letting your dog drink water from the sprinkler does not cost the park more money, because the same amount of water comes out of the sprinkler, whether some of the droplets land on the dog's tongue or whether they all falls on the ground.
• Some water is drawn in by the dog.

Often several dogs catch water drops on their tongues at the same time at the same fountain, and still the vast majority of the water is "wasted" landing on the ground. Likewise you can have thousands of people tuning in to the same TV station, and still the vast majority of the photons pouring out of the transmission antennas never hits a receiver antenna, but instead is "wasted" hitting trees or mountains or escaping to outer space. There is no way to tell from looking at the park's water meter whether dozens of dogs drink water from this fountain, or no dogs at all -- the same water comes out the sprinkler either way. There is no way to tell from looking at the broadcaster's electic meter whether thousands of people are tuned in, or no one is tuned in -- the same electromagnetic power comes out of the transmission tower either way.

This is very different from the way energy flows "through the air" in a air-core concentric-coil transformer, or "through the air" in an air dielectric capacitor, or the way mains powered devices "draw in" only the amount of current and power they need.

• Do radio receivers use any power from a transmitter?

A few crystal radios have no batteries or mains connection -- all the power they have comes from the radio transmitter, and the radio uses power from the transmitter to drive the earphone.

You could argue that most radios extract only the signal from the station; all the power from the antenna ends up warming the BE junction of the first transistor in the pre-amplifier, and 100% of the power "used" by the radio in later stages and to drive the speakers comes from batteries or mains power or a clockwork spring.

How much would make a difference? Well, if we packed enough radios and their antennas all around the broadcast antenna, eventually we would form a Faraday cage -- those radios would absorb all the broadcast energy, and other radios outside a Faraday cage cannot hear any transmissions from inside it.

There are a few things this analogy does not capture perfectly. Although it is tempting to think of the antenna as a "bucket", since the bigger it is the more photons it catches, a tuned antenna can catch far more energy than one might expect from its size and the local energy density -- 'Energy-sucking' Radio Antennas. If a puppy is catching the droplets on his tongue, and then a German Shepherd steps over him and catches the droplets first, then nothing reaches the puppy -- unless the puppy moves a bit to the side to get out of the shadow of the big dog. Likewise, if you put one radio antenna close to and immediately "behind" another radio antenna (as seen from the transmission tower), the upstream radio one will receive perfectly, as if the downstream radio is not even there, and the downstream radio will hear nothing -- until the downstream radio moves a bit to the side to get out of the shadow of the big dog. However, if you move the downstream radio antenna further away from (and yet still behind) the upstream antenna, it will also start to hear the station -- the power from the station "curves around" the upstream radio.

A typical FM broadcast tower puts out 100 kW ERP (+80 dBm) and 300 m high. FM radio receivers are expected to work down to a signal strength of 0.5mV/m. A typical radio reciever has a sensitivity of -90 dBm with an antenna roughly 1 m long.

Does the Sun create more energy when the cat lies on the windowsill?

That is correct; your statement about dissipation is about right, it just keeps radiating out into space or the distance. Think about light: everyone can look at a light source whether it can hit the walls or not, it doesn't draw any more power.

Some energy is received by the receiver, but this doesn't affect the transmitter.